線段樹的更新及完整程序

線段樹的更新

SegmentTree.java

     public void set(int index,E e){
        if(index<0||index>=data.length)
            throw new IllegalArgumentException("INDEX is illegal");
        data[index]=e;
        //更新tree
         set(0,0,data.length-1,index,e);

     }
     //在以treeIndex 爲根的線段樹中更新 INDEX 的值爲e
     private void set (int treeIndex,int l,int r,int index,E e){
        if(l==r&& l==index) {
            tree[treeIndex]=e;
            return ;
        }
        int TreeLeftIndex=leftChild(treeIndex);
        int TreeRightIndex=rightChild(treeIndex);
        int mid=l+(r-l)/2;
        if(index<=mid)
             set(TreeLeftIndex,l,mid,index,e );
        else
            set(TreeRightIndex,mid+1,r,index,e );
        tree[treeIndex]=merger.merge(tree[TreeLeftIndex],tree[TreeRightIndex]);
    }

線段樹的完整框架

public class SegmentTree<E> {
    private E[] tree;
    private E[] data;
    private Merger<E>merger;
    public SegmentTree(E[] arr,Merger<E> merger){
        this.merger=merger;
        data=(E[])new Object[arr.length];
        for(int i=0;i<arr.length;i++){
            data[i]=arr[i];
        }
        //用數組表示樹類型結構
        tree=(E[])new Object[4*arr.length];
        buildSegmentTree(0,0,data.length-1);//線段樹的根結點索引爲0
    }
    //遞歸構建索引爲樹結點treeindex 對應data區間[l,r]的信息
    public void buildSegmentTree(int treeindex,int l,int r){
        if(l==r){
            tree[treeindex]=data[l];
            return;
        }
        int treeleftchildindex=leftChild(treeindex);
        int treerightchildindex=rightChild(treeindex);
        int mid=l+(r-l)/2;
        buildSegmentTree(treeleftchildindex,l,mid);
        buildSegmentTree(treerightchildindex,mid+1,r);
//        tree[treeindex]=+
        tree[treeindex]=merger.merge(tree[treeleftchildindex],tree[treerightchildindex]);
    }
    public int getSize(){
        return data.length;
    }
    public E get(int index){
        if(index<0||index>=data.length)
            throw new IllegalArgumentException("index is illeagal");
        return data[index];
    }
    public int leftChild(int index){
        return 2*index +1;
    }
    public int rightChild(int index){
        return 2* index +2;
    }
    public E query(int queryL,int queryR){
        if(queryL<0||queryL>=data.length||queryR<0||queryR>=data.length||queryL>queryR)
            throw new IllegalArgumentException("index illegal");
        return query(0,0,data.length-1,queryL,queryR);
    }
    //從線段樹的treeIndex 索引開始在區間data[l:r]查找queryL,queryR 的值
    private E query(int treeIndex,int l,int r,int queryL,int queryR){
        if(l==queryL && r==queryR){
            return tree[treeIndex];
        }
        int mid=l+(r-l)/2;
        if( queryR<=mid)
            return query(leftChild(treeIndex),l,mid,queryL,queryR);
        else if(queryL>=mid+1)
            return query(rightChild(treeIndex),mid+1,r,queryL,queryR);
        return merger.merge(query(leftChild(treeIndex),l,mid,queryL,mid),query(rightChild(treeIndex),mid+1,r,mid+1,queryR));}
     public void set(int index,E e){
        if(index<0||index>=data.length)
            throw new IllegalArgumentException("INDEX is illegal");
        data[index]=e;
        //更新tree
         set(0,0,data.length-1,index,e);

     }
     //在以treeIndex 爲根的線段樹中更新 INDEX 的值爲e
     private void set (int treeIndex,int l,int r,int index,E e){
        if(l==r&& l==index) {
            tree[treeIndex]=e;
            return ;
        }
        int TreeLeftIndex=leftChild(treeIndex);
        int TreeRightIndex=rightChild(treeIndex);
        int mid=l+(r-l)/2;
        if(index<=mid)
             set(TreeLeftIndex,l,mid,index,e );
        else
            set(TreeRightIndex,mid+1,r,index,e );
        tree[treeIndex]=merger.merge(tree[TreeLeftIndex],tree[TreeRightIndex]);
    }
    @Override
    public String toString(){
        StringBuilder res=new StringBuilder();
        res.append('[');
        for(int i=0;i<tree.length;i++){
            if(tree[i]!=null) res.append(tree[i]);
            else res.append("null");
            if(i!=tree.length-1) res.append(" ");
        }
        res.append(']');
        return res.toString();
    }
}

線段 樹應用場景接口

Merge.java

public interface Merger<E> {
    E merge(E a,E b);
}

線段樹的調用

main.java

public class Main {

    public static void main(String[] args) {
        Integer[] nums={-2,0,3,-5,2,-1};
        //匿名類
        Merger<Integer> merger=new Merger<Integer>() {
            @Override
            public Integer merge(Integer a, Integer b) {
                return a+b;
            }
        };
        SegmentTree<Integer>segTree=new SegmentTree<>(nums,merger);
        SegmentTree<Integer>segTree2=new SegmentTree<>(nums,(a,b)->a+b);//lambda 表達式
        System.out.println(segTree.toString());
        System.out.println(segTree.query(0,2));
//        System.out.println(segTree.query(0,5));
    }
}